From Eternity to Here: The Quest for the Ultimate Theory of Time

by Sean M. Carroll

  —St. Augustine, Confessions

  The next time you find yourself in a bar, or on an airplane, or standing in line at the Department of Motor Vehicles, you can pass the time by asking the strangers around you how they would define the word time. That’s what I started doing, anyway, as part of my research for this book. You’ll probably hear interesting answers: “Time is what moves us along through life,” “Time is what separates the past from the future,” “Time is part of the universe,” and more along those lines. My favorite was “Time is how we know when things happen.”

  All of these concepts capture some part of the truth. We might struggle to put the meaning of “time” into words, but like St. Augustine we nevertheless manage to deal with time pretty effectively in our everyday lives. Most people know how to read a clock, how to estimate the time it will take to drive to work or make a cup of coffee, and how to manage to meet their friends for dinner at roughly the appointed hour. Even if we can’t easily articulate what exactly it is we mean by “time,” its basic workings make sense at an intuitive level.

  Like a Supreme Court justice confronted with obscenity, we know time when we see it, and for most purposes that’s good enough. But certain aspects of time remain deeply mysterious. Do we really know what the word means?

  WHAT WE MEAN BY TIME

  The world does not present us with abstract concepts wrapped up with pretty bows, which we then must work to understand and reconcile with other concepts. Rather, the world presents us with phenomena, things that we observe and make note of, from which we must then work to derive concepts that help us understand how those phenomena relate to the rest of our experience. For subtle concepts such as entropy, this is pretty clear. You don’t walk down the street and bump into some entropy; you have to observe a variety of phenomena in nature and discern a pattern that is best thought of in terms of a new concept you label “entropy.” Armed with this helpful new concept, you observe even more phenomena, and you are inspired to refine and improve upon your original notion of what entropy really is.

  For an idea as primitive and indispensable as “time,” the fact that we invent the concept rather than having it handed to us by the universe is less obvious—time is something we literally don’t know how to live without. Nevertheless, part of the task of science (and philosophy) is to take our intuitive notion of a basic concept such as “time” and turn it into something rigorous. What we find along the way is that we haven’t been using this word in a single unambiguous fashion; it has a few different meanings, each of which merits its own careful elucidation.

  Time comes in three different aspects, all of which are going to be important to us.

  1. Time labels moments in the universe.

  Time is a coordinate; it helps us locate things.

  2. Time measures the duration elapsed between events.

  Time is what clocks measure.

  3. Time is a medium through which we move.

  Time is the agent of change. We move through it, or—equivalently—time flows past us, from the past, through the present, toward the future.

  At first glance, these all sound somewhat similar. Time labels moments, it measures duration, and it moves from past to future—sure, nothing controversial about any of that. But as we dig more deeply, we’ll see how these ideas don’t need to be related to one another—they represent logically independent concepts that happen to be tightly intertwined in our actual world. Why that is so? The answer matters more than scientists have tended to think.

  1. Time labels moments in the universe

  John Archibald Wheeler, an influential American physicist who coined the term black hole, was once asked how he would define “time.” After thinking for a while, he came up with this: “Time is Nature’s way of keeping everything from happening at once.”

  There is a lot of truth there, and more than a little wisdom. When we ordinarily think about the world, not as scientists or philosophers but as people getting through life, we tend to identify “the world” as a collection of things, located in various places. Physicists combine all of the places together and label the whole collection “space,” and they have different ways of thinking about the kinds of things that exist in space—atoms, elementary particles, quantum fields, depending on the context. But the underlying idea is the same. You’re sitting in a room, there are various pieces of furniture, some books, perhaps food or other people, certainly some air molecules—the collection of all those things, everywhere from nearby to the far reaches of intergalactic space, is “the world.”

  And the world changes. We find objects in some particular arrangement, and we also find them in some other arrangement. (It’s very hard to craft a sensible sentence along those lines without referring to the concept of time.) But we don’t see the different configurations “simultaneously,” or “at once.” We see one configuration—here you are on the sofa, and the cat is in your lap—and then we see another configuration—the cat has jumped off your lap, annoyed at the lack of attention while you are engrossed in your book. So the world appears to us again and again, in various configurations, but these configurations are somehow distinct. Happily, we can label the various configurations to keep straight which is which—Miss Kitty is walking away “now”; she was on your lap “then.” That label is time.

  So the world exists, and what is more, the world happens, again and again. In that sense, the world is like the different frames of a film reel—a film whose camera view includes the entire universe. (There are also, as far as we can tell, an infinite number of frames, infinitesimally separated.) But of course, a film is much more than a pile of individual frames. Those frames better be in the right order, which is crucial for making sense of the movie. Time is the same way. We can say much more than “that happened,” and “that also happened,” and “that happened, too.” We can say that this happened before that happened, and the other thing is going to happen after. Time isn’t just a label on each instance of the world; it provides a sequence that puts the different instances in order.

  A real film, of course, doesn’t include the entire universe within its field of view. Because of that, movie editing typically involves “cuts”—abrupt jumps from one scene or camera angle to another. Imagine a movie in which every single transition between two frames was a cut to a completely different scene. When shown through a projector, it would be incomprehensible—on the screen it would look like random static. Presumably there is some French avant-garde film that has already used this technique.

  The real universe is not an avant-garde film. We experience a degree of continuity through time—if the cat is on your lap now, there might be some danger that she will stalk off, but there is little worry that she will simply dematerialize into nothingness one moment later. This continuity is not absolute, at the microscopic level; particles can appear and disappear, or at least transform under the right conditions into different kinds of particles. But there is not a wholesale rearrangement of reality from moment to moment.

  This phenomenon of persistence allows us to think about “the world” in a different way. Instead of a collection of things distributed through space that keep changing into different configurations, we can think of the entire history of the world, or any particular thing in it, in one fell swoop. Rather than thinking of Miss Kitty as a particular arrangement of cells and fluids, we can think of her entire life stretching through time, from birth to death. The history of an object (a cat, a planet, an electron) through time defines its world line—the trajectory the object takes through space as time passes.3 The world line of an object is just the complete set of positions the object has in the world, labeled by the particular time it was in each position.

  Figure 1: The world, ordered into different moments of time. Objects (including people and cats) persist from moment to moment, defining world lines that stretch through time.

  Finding ourselves

  Thinking of the entire history of the universe all at o
nce, rather than thinking of the universe as a set of things that are constantly moving around, is the first step toward thinking of time as “kind of like space,” which we will examine further in the chapters to come. We use both time and space to help us pinpoint things that happen in the universe. When you want to meet someone for coffee, or see a certain showing of a movie, or show up for work along with everyone else, you need to specify a time: “Let’s meet at the coffee shop at 6:00 P.M. this Thursday.”

  If you want to meet someone, of course, it’s not sufficient just to specify a time; you also need to specify a place. (Which coffee shop are we talking about here?) Physicists say that space is “three-dimensional.” What that means is that we require three numbers to uniquely pick out a particular location. If the location is near the Earth, a physicist might give the latitude, longitude, and height above ground. If the location is somewhere far away, astronomically speaking, we might give its direction in the sky (two numbers, analogous to latitude and longitude), plus the distance from Earth. It doesn’t matter how we choose to specify those three numbers; the crucial point is that you will always need exactly three. Those three numbers are the coordinates of that location in space. We can think of a little label attached to each point, telling us precisely what the coordinates of that point are.

  Figure 2: Coordinates attached to each point in space.

  In everyday life, we can often shortcut the need to specify all three coordinates of space. If you say “the coffee shop at Eighth and Main Street,” you’re implicitly giving two coordinates—“Eighth” and “Main Street”—and you’re assuming that we all agree the coffee shop is likely to be at ground level, rather than in the air or underground. That’s a convenience granted to us by the fact that much of the space we use to locate things in our daily lives is effectively two-dimensional, confined near the surface of the Earth. But in principle, all three coordinates are needed to specify a point in space.

  Each point in space occurs once at each moment of time. If we specify a certain location in space at one definite moment in time, physicists call that an event. (This is not meant to imply that it’s an especially exciting event; any random point in empty space at any particular moment of time would qualify, so long as it’s uniquely specified.) What we call the “universe” is just the set of all events—every point in space, at every moment of time. So we need four numbers—three coordinates of space, and one of time—to uniquely pick out an event. That’s why we say that the universe is four-dimensional. This is such a useful concept that we will often treat the whole collection, every point in space at every moment of time, as a single entity called spacetime.

  This is a big conceptual leap, so it’s worth pausing to take it in. It’s natural to think of the world as a three-dimensional conglomeration that keeps changing (“happening over and over again, slightly differently each time”). We’re now suggesting that we can think of the whole shebang, the entire history of the world, as a single four-dimensional thing, where the additional dimension is time. In this sense, time serves to slice up the four-dimensional universe into copies of space at each moment in time—the whole universe at 10:00 A.M. on January 20, 2010; the whole universe at 10:01 A.M. on January 20, 2010; and so on. There are an infinite number of such slices, together making up the universe.

  2. Time measures the duration elapsed between events

  The second aspect of time is that it measures the duration elapsed between events. That sounds pretty similar to the “labels moments in the universe” aspect already discussed, but there is a difference. Time not only labels and orders different moments; it also measures the distance between them.

  When taking up the mantle of philosopher or scientist and trying to make sense of a subtle concept, it’s helpful to look at things operationally—how do we actually use this idea in our experience? When we use time, we refer to the measurements that we get by reading clocks. If you watch a TV show that is supposed to last one hour, the reading on your clock at the end of the show will be one hour later than what it read when the show began. That’s what it means to say that one hour elapsed during the broadcast of that show: Your clock read an hour later when it ended than when it began.

  But what makes a good clock? The primary criterion is that it should be consistent—it wouldn’t do any good to have a clock that ticked really fast sometimes and really slowly at others. Fast or slow compared to what? The answer is: other clocks. As a matter of empirical fact (rather than logical necessity), there are some objects in the universe that are consistently periodic—they do the same thing over and over again, and when we put them next to one another we find them repeating in predictable patterns.

  Think of planets in the Solar System. The Earth orbits around the Sun, returning to the same position relative to the distant stars once every year. By itself, that’s not so meaningful—it’s just the definition of a “year.” But Mars, as it turns out, returns to the same position once every 1.88 years. That kind of statement is extremely meaningful—without recourse to the concept of a “year,” we can say that Earth moves around the Sun 1.88 times every time Mars orbits just once.4 Likewise, Venus moves around the Sun 1.63 times every time Earth orbits just once.

  The key to measuring time is synchronized repetition—a wide variety of processes occur over and over again, and the number of times that one process repeats itself while another process returns to its original state is reliably predictable. The Earth spins on its axis, and it’s going to do so 365.25 times every time the Earth moves around the Sun. The tiny crystal in a quartz watch vibrates 2,831,155,200 times every time the Earth spins on its axis. (That’s 32,768 vibrations per second, 3,600 seconds in an hour, 24 hours in a day.5) The reason why quartz watches are reliable is that quartz crystal has extremely regular vibrations; even as the temperature or pressure changes, the crystal will vibrate the same number of times for every one rotation of the Earth.

  So when we say that something is a good clock, we mean that it repeats itself in a predictable way relative to other good clocks. It is a fact about the universe that such clocks exist, and thank goodness. In particular, at the microscopic level where all that matters are the rules of quantum mechanics and the properties (masses, electric charges) of individual elementary particles, we find atoms and molecules that vibrate with absolutely predictable frequencies, forming a widespread array of excellent clocks marching in cheerful synchrony. A universe without good clocks—in which no processes repeated themselves a predictable number of times relative to other repeating processes—would be a scary universe indeed.6

  Still, good clocks are not easy to come by. Traditional methods of timekeeping often referred to celestial objects—the positions of the Sun or stars in the sky—because things down here on Earth tend to be messy and unpredictable. In 1581, a young Galileo Galilei reportedly made a breakthrough discovery while he sat bored during a church service in Pisa. The chandelier overhead would swing gently back and forth, but it seemed to move more quickly when it was swinging widely (after a gust of wind, for example) and more slowly when wasn’t moving as far. Intrigued, Galileo decided to measure how much time it took for each swing, using the only approximately periodic event to which he had ready access: the beating of his own pulse. He found something interesting: The number of heartbeats between swings of the chandelier was roughly the same, regardless of whether the swings were wide or narrow. The size of the oscillations—how far the pendulum swung back and forth—didn’t affect the frequency of those oscillations. That’s not unique to chandeliers in Pisan churches; it’s a robust property of the kind of pendulum physicists call a “simple harmonic oscillator.” And that’s why pendulums form the centerpiece of grandfather clocks and other timekeeping devices: Their oscillations are extremely reliable. The craft of clock making involves the search for ever-more-reliable forms of oscillations, from vibrations in quartz to atomic resonances.

  Our interest here is not really in the intricacies of clock constructio
n, but in the meaning of time. We live in a world that contains all sorts of periodic processes, which repeat a predictable number of times in comparison to certain other periodic processes. And that’s how we measure duration: by the number of repetitions of such a process. When we say that our TV program lasts one hour, we mean that the quartz crystal in our watch will oscillate 117,964,800 times between the start and end of the show (32,768 oscillations per second, 3,600 seconds in an hour).

  Notice that, by being careful about defining time, we seem to have eradicated the concept entirely. That’s just what any decent definition should do—you don’t want to define something in terms of itself. The passage of time can be completely recast in terms of certain things happening together, in synchrony. “The program lasts one hour” is equivalent to “there will be 117,964,800 oscillations of the quartz crystal in my watch between the beginning and end of the program” (give or take a few commercials). If you really wanted to, you could reinvent the entire superstructure of physics in a way that completely eliminated the concept of “time,” by replacing it with elaborate specifications of how certain things happen in coincidence with certain other things.7 But why would we want to? Thinking in terms of time is convenient, and more than that, it reflects a simple underlying order in the way the universe works.

  Figure 3: Good clocks exhibit synchronized repetition. Every time one day passes, the Earth rotates once about its axis, a pendulum with a period of 1 second oscillates 86,400 times, and a quartz watch crystal vibrates 2,831,155,200 times.

  Slowing, stopping, bending time

  Armed with this finely honed understanding of what we mean by the passage of time, at least one big question can be answered: What would happen if time were to slow down throughout the universe? The answer is: That’s not a sensible question to ask. Slow down relative to what? If time is what clocks measure, and every clock were to “slow down” by the same amount, it would have absolutely no effect at all. Telling time is about synchronized repetition, and as long as the rate of one oscillation is the same relative to some other oscillation, all is well.